today's lesson:
January 8, 2014
(all answers at the end of explanation)
Integers not only have adding in them, but subtracting, or removing. A rule you must know is "Whenever something is not there, you must add a zero pair"(all answers at the end of explanation)
A stragety you can use when you want to recongnize when to say "and" (add or combine) or "remove" is when the equation is a double negative or it's a negative and a negative, if not, then always combine unless you remove a negative (negative and negative). When you have a negative and a negative, you must add a zero pair since that negative isn't there.
negative minus negative (with brackets)
For example, (5)  (6) =For the words, it would be :
Owe 5 Remove Owe 6.
Since you are trying to remove (6), you can't since there isn't so you do a zero pair.
++++++
      < This evens them out and then you remove the (6) so you are left with positive 6.
Here you would remove the (6) since it's part of the equation.
Then you combine (5) since integers is all about combining.
+ + + + + +
    
You have one positive left over, therefore, the answer is (+1) or have 1.
positive minus negative (no brackets)
And example for a positive minus negative equation is:
9  1 =
This may seem like a regular subtracting question, but it really is like saying (+ 9)  (1).
The minus sign actually is part of the one since it means that the one is negative.
A way this might be easier is to say the equation out loud or put it in words like so:
have 9, owe 1.
To show this you would have 9 positives (have is positive), and 1 negative (owe is negative).
+ + + + + + + + +

The zero pair cancels one of the positives and one of the negatives, leaving behind only 8 positives. The answer would be (+8) or have 8.
negative minus negative ( first one has no brackets)
This may seem different from the first one, but it's all about how you look at it.
An example of this type is : 4  (6) =
The only difference for this is that the negative 4 doesn't have brackets.
In words this would be : Owe 4 REMOVE Owe 6.
In pictures or in integer chips this would be 6 zero pairs, removing the minus, and you add the positives with the negative which is negative 4.
     
+ + + + + +
Then COMBINE the positive 6 with the negative 4.
+ + + + + +
   
Then you have 2 positives left over which gives you your answer of (+2).
It goes with positive minus negative, example: 4(6)
positive minus negative (with brackets)
An example of positive minus negative would be:
7(6) =
In words this would be have 7 REMOVE owe 6. This a double negative, since there are two negatives together.
+ + + + + +
     
Then you combine the 6 positives together with the 7 positives, which equals 13.
Calculate with the zero pairs and you're done. You have one positive left over, and you answer is (+1) or have 1.
if that didn't work, here's a video.
here's some more fun with subtracting integers (game)
(if that didn't work try copying this link)
Good luck on your learning!
Thanks for the help! The examples really helped me to get a better chance of solving different equations and the game along with the video was also extra helpful! (:
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